100x-60x^2=40

Solution for 100x-60x^2=40 equation:

100x-60x^2=40

We move all terms to the left:

100x-60x^2-(40)=0

a = -60; b = 100; c = -40;
Δ = b2-4ac
Δ = 1002-4·(-60)·(-40)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20}{2*-60}=\frac{-120}{-120}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20}{2*-60}=\frac{-80}{-120}
=2/3
$